Bounding back and forth through the complex field

15 October 2004
Alex Wilkie
The first seminar will be given with the new students in mind. It will begin with a brief overview of quantifier elimination and its relation to the back-and-forth property.I shall then discuss complexity issues with particular reference to algebraically closed fields.In particular,how much does the height and degree of polynomials in a formula increase when a quantifier is eliminated? The precise answer here gave rise to the definition of a `generic' transcendental entire function,which will also be discussed.